Problem: $A$ $B$ $C$ If: $ AC = 96$, $ BC = 3x + 6$, and $ AB = 6x + 9$, Find $BC$.
Explanation: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {6x + 9} + {3x + 6} = {96}$ Combine like terms: $ 9x + 15 = {96}$ Subtract $15$ from both sides: $ 9x = 81$ Divide both sides by $9$ to find $x$ $ x = 9$ Substitute $9$ for $x$ in the expression that was given for $BC$ $ BC = 3({9}) + 6$ Simplify: $ {BC = 27 + 6}$ Simplify to find ${BC}$ : $ {BC = 33}$